Comparative application of multi-criteria decision-making methods in determining availing level (Case study: districts of Kamyaran County)

Introduction
One of the common ways to prioritize the options which has become increasingly developed in recent years, is using multi-criteria decision-making methods. In multi-criteria decision-making issues, the targeted options are prioritized with regard various indicators that may sometimes conflict with each other (Poortahery, 1393: 20). These methods provide simple and intuitive tools for decision-making about issues that involve non-conclusive, and mostly subjective data. In fact, these methods have developed since the early 1970s which today has become quite prevalent (Jin & lei, 2005,61-64). The reason can be seen in the fact that such techniques are easily understandable for different users. Moreover, unlike mathematical models of planning and decision-making that do not include qualitative variables in the modeling, these techniques have the ability to include both qualitative and quantitative variables simultaneously in the decision-making process which in turn expands the scope of application of these techniques (Ataei, 1385:87).
Methodology
The research method used in this research is descriptive-analytical. Documentary method has also been used for collecting the data in the study. The population of the study includes the districts of Kamyaran County in Kurdistan Province. On this basis, the theoretical principles related to the subject matter have been investigated using the secondary research method. In order for investigation and comparison of methods of assessing the level of availing, four methods of TOPSIS, taxonomy, simple analytic hierarchy process, and weighted sum model have been utilized. These methods have also been used to determine the degree of availing of the districts of Kamyaran County. To assess availing level of the districts of Kamyaran County, 16 indicators have been used.
Research findings
To determine the level of availing of the districts of Kamyaran County, after doing the three aforementioned stages, the findings that resulted from these stages were analyzed using multi-criteria methods which were mentioned earlier. The findings resulted from the above methods are as follows:
Table 1: Results of application of TOPSIS model
Gavrood Avalan Sorsor Amirabad Shahou Chavrood Bilvar District
0/475 0/262 0/311 0/382 0/377 0/702 0/443 Coefficient of expansion
2 7 6 4 5 1 3 Rank


Table 2: Results of application of WSM model
Gavrood Avalan Sorsor Amirabad Shahou Chavrood Bilvar District
126/79 41/34 53/79 84/54 79/56 207/97 116/61 Coefficient of expansion
2 7 6 4 5 1 3 Rank


Table 3: results of application of SAW model
Gavrood Avalan Sorsor Amirabad Shahou Chavrood Bilvar District
0/2163 0/0671 0/0848 0/0776 0/1331 0/2950 0/1406 Coefficient of expansion
2 7 5 6 4 1 3 Rank

The results of applying multi-criteria methods in this study showed that regarding the ranking, the districts of Kamyaran County do not have fixed and similar positions.
Prioritization Strategy
In using different methods of prioritization, decision-maker may be confronted with a situation that in a real issue, a united ranking is not reached from application of various methods regarding alternatives. In that case, it is necessary for the decision-makers to use integrated approaches, such as mean of ranks, or Breda and Cap Land Methods for final decision making. In this study, mean of ranks method has been used for the final rating. Final rankings of the districts under study can be calculated using the mean of ranks method. Mean of ranks can be calculated from the sum of rankings and dividing them by the number of used methods (Poortahery, 1393,182).

Table 5: Calculation of mean rank of multi-criteria methods under study
Districts TOPSIS SAW WSM Mean Rank
Gavrood 1 1 1 1
Ghavrood 2 2 2 2
Bilvar 3 3 3 3
Amir Abad 4 6 4 4/66
Shahou 5 4 5 4/66
Sorsor 6 5 6 5/66
Avalan 7 7 7 7
Reference: author's calculations

Conclusion
The results of applying four multi-criteria decision-making methods in this study indicated that the positions of the districts of Kamyaran County are not the same with regard to the availing; for example, the district of Amirabad in taxonomy and weighted sum models had the first rank whereas in TOPSIS and SAW models had the second rank. The results of this study have shown that the position of each of the districts studied by multi-criteria methods of Numerical Taxonomy, TOPSIS, WSM, and SAW, is not the same. Moreover, in the above mentioned methods, TOPSIS and simple WSM methods with 14/28 had the lowest percentage of changes and SAW method with 28/56 had the highest percentage of change among the methods under study. Regarding the level of availing, districts of Amirabad, Gavrood, Bilvar and Zhavrood are in the praprofiting level, district of AmirAbad and Shahou is in the mesoprfiting level, and the districts of Avalan and Sorsor are in unprofitinglevel.